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From: G. L. Bradford on 4 Aug 2010 06:16

"PD" <thedraperfamily(a)gmail.com> wrote in message
news:8babe3ec-6133-4a2d-be14-b1127176ddc2(a)i24g2000yqa.googlegroups.com...
On Aug 2, 11:16 am, eric gisse <jowr.pi.nos...(a)gmail.com> wrote:
> Sam Wormley wrote:
> > I gave a presentation yesterday to an audience that included
> > one of my retired physics professors. I had responded to a
> > question during the presentation saying that the universe could
> > be infinite, but that since we cannot observe it, we cannot say
> > for sure.
>
> > After the presentation, Barney Cook, said I was wrong, that
> > the the measured flatness of the universe means the universe
> > is infinite.
>
> > I would appreciate comments from the physicists here. Thanks.
> > -Sam
>
> I'd ask him why measured spatial flatness implies an infinite universe,
> given that such a state can start from a finite amount of time ago.

That doesn't mean anything. You can have an infinite universe with a
finite lifetime.
Basic analogy: Imagine an infinite line. Take a point on the line and
observe that another point at distance x from it is receding with
velocity v, a third point at distance 2x is receding with velocity 2v,
and a point at distance nx is receding with velocity nv. This
*infinite* line will have have all had to diverge from a single point
at time x/v ago, provided that all the velocities do not change.

=====================

Apparently no one saw the key, except Sam who used it: "Since we cannot
observe it." (Neither the infinitely 'BROAD' nor the infinitely 'DEEP'! Nor
the infinitely infinitesimal, including the infinity -- the countless
plurality -- of infinitesimals!)

---------------------------
Constant: infinite Singularity
(of countless singularities...)
(...Broad and Deep!)
<><><><><><><><>
Constant: Planck base / ...
(... / horizon / plane / ...)
(... / singularity / universe / ...)
<><><><><><><><>
Constant: infinite Universe
(of countless universes...)
(...Broad and Deep!)
---------------------------

And by the way, not one -- not a single one! -- of those 'points' in the
"observable universe" is in exactly the same space-time universe. Each of
the points is in an individually flat 2-d space-time universe slightly to
enormously offsetting in space-time (in history) from all the others.

You drew a very different picture implying a very different universe: End
to end a very [singular] reality of environmental universe that all the
points CURRENTLY exist in to fly apart in. You couldn't be farther from the
reality. Instead of an observation of multiple points flying apart in a
SINGLE universe, the real observation should be an observation of countless
flat-panel 2-d space-time universes (relatively speaking, 'histories')
regressively and progressively offsetting in space-time.

You seem to be trying to force just one, single, space-time universe upon
us when there are actually too many space-time universes (too many
space-time horizons) to count just from our own local ( | | | | ), or any
of an infinity of locals ( | | | | ), to the most distant non-local
[macro-verse / micro-verse] horizon ( | | | | ) ( |||| ) ( || ) ( | ) ( : )
( ) observable from any of them. (It being precisely one and the same [most
distant] horizon point whether macroscopic or microscopic universe, the
Planck base / horizon / .....)

GLB

==================

From: srp on 4 Aug 2010 09:09
On 3 août, 19:08, Sam Wormley <sworml...(a)gmail.com> wrote:
> On 8/3/10 12:41 PM, PD wrote:
>
>
>
> > On Aug 2, 2:40 pm, Sam Wormley<sworml...(a)gmail.com>  wrote:
> >> I gave a presentation yesterday to an audience that included
> >> one of my retired physics professors. I had responded to a
> >> question during the presentation saying that the universe could
> >> be infinite, but that since we cannot observe it, we cannot say
> >> for sure.
>
> >> After the presentation, Barney Cook, said I was wrong, that
> >> the the measured flatness of the universe means the universe
> >> is infinite.
>
> >> I would appreciate comments from the physicists here. Thanks.
> >> -Sam
>
> > A flat universe can only be finite if it has a boundary.
> > A finite universe can only be boundariless if it is curved.
>
> > So it really hinges on whether there is a boundary.
>
>    Good Point!

I see you gently retract into talking only about theories.

You just had a brush with what is awaiting anyone
publicly indulging into career threatening talks
about the physical reality that needs to be explored
further and that underlies all community approved theories,
however defective or appropriate they may be.

First, hints that you are going astray, then, warnings
that you need to dig back into your community approved
literature, then, general cold shouldering and possibly
loss of tenure.

Luckily for you, you seem to have reacted "properly" to the
first hint.

André Michaud

From: carlip-nospam on 9 Aug 2010 16:24
Sam Wormley <swormley1(a)gmail.com> wrote:
> I gave a presentation yesterday to an audience that included
> one of my retired physics professors. I had responded to a
> question during the presentation saying that the universe could
> be infinite, but that since we cannot observe it, we cannot say
> for sure.

> After the presentation, Barney Cook, said I was wrong, that
> the the measured flatness of the universe means the universe
> is infinite.

This is not correct, for two reasons:

1. We can't measure the spatial curvature of the Universe exactly
-- there is no way to know whether it is zero or just smaller than
our current resolution. (I don't know of any way to determine this
even in principle.) So, for instance, while a spatial three-sphere
has positive curvature, a sphere with a large enough radius of
curvature can have an arbitrarily small positive curvature.

(Note that this doesn't work the other way. We *could*, in principle,
measure a positive or negative curvature accurately enough to exclude
the possibility of flatness.)

2. Even if the Universe is spatially flat, that would not imply an
infinite size. While infinite flat space is the simplest possibility,
it is not unique. For example, in two dimensions, a cylinder is flat
(that is, the axioms of Euclidean geometry hold, which is essentially
what we measure). A torus can be given a flat metric; so can a Klein
bottle. This is equally true for the three-dimensional generalizations
of these topologies.

We might hope to observe whether the Universe has, for example, the
topology of a torus. If it does, we might be able to see "around" a
circumference -- that is, the Universe might look identical in two
opposite directions. This is tricky, since the light travel time to a
given object would be different in the two directions, so we would
see it at two different ages, but there are interesting ideas about how
to sort this out. Again, though, while we could conceivably detect
a torus topology, we could never disprove the possibility -- if the
circumferences of the torus were large enough, light would not have
had time to travel all the way around in the age of the Universe, so
the topology would be essentially invisible.

Steve Carlip


From: Sam Wormley on 9 Aug 2010 16:31
On 8/9/10 3:24 PM, carlip-nospam(a)physics.ucdavis.edu wrote:
> Sam Wormley<swormley1(a)gmail.com> wrote:
>> I gave a presentation yesterday to an audience that included
>> one of my retired physics professors. I had responded to a
>> question during the presentation saying that the universe could
>> be infinite, but that since we cannot observe it, we cannot say
>> for sure.
>
>> After the presentation, Barney Cook, said I was wrong, that
>> the the measured flatness of the universe means the universe
>> is infinite.
>
> This is not correct, for two reasons:
>
> 1. We can't measure the spatial curvature of the Universe exactly
> -- there is no way to know whether it is zero or just smaller than
> our current resolution. (I don't know of any way to determine this
> even in principle.) So, for instance, while a spatial three-sphere
> has positive curvature, a sphere with a large enough radius of
> curvature can have an arbitrarily small positive curvature.
>
> (Note that this doesn't work the other way. We *could*, in principle,
> measure a positive or negative curvature accurately enough to exclude
> the possibility of flatness.)
>
> 2. Even if the Universe is spatially flat, that would not imply an
> infinite size. While infinite flat space is the simplest possibility,
> it is not unique. For example, in two dimensions, a cylinder is flat
> (that is, the axioms of Euclidean geometry hold, which is essentially
> what we measure). A torus can be given a flat metric; so can a Klein
> bottle. This is equally true for the three-dimensional generalizations
> of these topologies.
>
> We might hope to observe whether the Universe has, for example, the
> topology of a torus. If it does, we might be able to see "around" a
> circumference -- that is, the Universe might look identical in two
> opposite directions. This is tricky, since the light travel time to a
> given object would be different in the two directions, so we would
> see it at two different ages, but there are interesting ideas about how
> to sort this out. Again, though, while we could conceivably detect
> a torus topology, we could never disprove the possibility -- if the
> circumferences of the torus were large enough, light would not have
> had time to travel all the way around in the age of the Universe, so
> the topology would be essentially invisible.
>
> Steve Carlip
>
>

Thank You!
-Sam


From: PD on 9 Aug 2010 16:34
On Aug 9, 3:24 pm, carlip-nos...(a)physics.ucdavis.edu wrote:
> Sam Wormley <sworml...(a)gmail.com> wrote:
> > I gave a presentation yesterday to an audience that included
> > one of my retired physics professors. I had responded to a
> > question during the presentation saying that the universe could
> > be infinite, but that since we cannot observe it, we cannot say
> > for sure.
> > After the presentation, Barney Cook, said I was wrong, that
> > the the measured flatness of the universe means the universe
> > is infinite.
>
> This is not correct, for two reasons:
>
> 1.  We can't measure the spatial curvature of the Universe exactly
> -- there is no way to know whether it is zero or just  smaller than
> our current resolution.  (I don't know of any way to determine this
> even in principle.)  So, for instance, while a spatial three-sphere
> has positive curvature, a sphere with a large enough radius of
> curvature can have an arbitrarily small positive curvature.
>
> (Note that this doesn't work the other way.  We *could*, in principle,
> measure a positive or negative curvature accurately enough to exclude
> the possibility of flatness.)
>
> 2.  Even if the Universe is spatially flat, that would not imply an
> infinite size.  While infinite flat space is the simplest possibility,
> it is not unique.  For example, in two dimensions, a cylinder is flat
> (that is, the axioms of Euclidean geometry hold, which is essentially
> what we measure).  A torus can be given a flat metric; so can a Klein
> bottle.  This is equally true for the three-dimensional generalizations
> of these topologies.
>
> We might hope to observe whether the Universe has, for example, the
> topology of a torus.  If it does, we might be able to see "around" a
> circumference -- that is, the Universe might look identical in two
> opposite directions.  This is tricky, since the light travel time to a
> given object would be different in the two directions, so we would
> see it at two different ages, but there are interesting ideas about how
> to sort this out.  Again, though, while we could conceivably detect
> a torus topology, we could never disprove the possibility -- if the
> circumferences of the torus were large enough, light would not have
> had time to travel all the way around in the age of the Universe, so
> the topology would be essentially invisible.
>
> Steve Carlip

Thanks, Steve. I learned something.
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